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Prove that cos^(-1)x+cos^(-1) [x/2 +(s...

Prove that `cos^(-1)x+cos^(-1) [x/2 +(sqrt(3-3x^(2)))/2 ] = pi/3 ` ,`1/2 le x le 1 `

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MODERN PUBLICATION-INVERSE - TRIGONOMETRIC FUNCTIONS-Frequently Asked Questions
  1. Prove that: 3sin^(-1)x=sin^(-1)(3x-4x^3), x in [-1/2,1/2]

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  2. If sin^(-1) x = tan^(-1)ym what is the value of (1)/(x^(2))-(1)/(y^(2)...

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  3. Prove that cos^(-1)x+cos^(-1) [x/2 +(sqrt(3-3x^(2)))/2 ] = pi/3 ,1...

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  4. Find the value of : sin^() (2 tan^(-1). 1/4) +cos (tan^(-1)2sqrt(2))

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  5. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

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  6. Show that sin^(-1)3/5-sin^(-1)8/(17)=cos^(-1)(84)/(85) .

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  7. Prove that: sin^(-1)((5)/(13))+cos^(-1)((4)/(5))=(1)/(2)sin^(-1)((3696...

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  8. Show that : 2 sin^(-1) (3/5)-tan^(-1) (17/31) = pi/4

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  9. Prove that tan[pi/4+1/2cos^(-1)""a/b]+tan[pi/4-1/2cos^(-1)""a/b]=2b/a

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  10. (9pi)/(8)-(9)/(4)sin^(-1)""(1)/(3)=(9)/(4)sin^(-1)""(2sqrt(2))/(3) (...

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  11. Prove that tan^(- 1)((6x-8x^3)/(1-12 x^2))-tan^(- 1)((4x)/(1-4x^2))=ta...

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  12. Prove that tan ^(-1) . 1/5 + tan^(-1) . 1/7 + tan ^(-1) . 1/8 = pi/4

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  13. Solve : 2 tan^(-1), (cos x) = tan^(-1), (2 cosec x)

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  14. Solve : tan^(-1) 4x +tan^(-1)6x = pi/4

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  15. If tan^-1 ((x-3)/(x-4))+tan^-1((x+3)/(x+4))=pi/4,

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  16. Solve : (i)" "tan^(-1). x/2 +tan^(-1). x/3 = pi/4 , sqrt(6) gt x gt 0...

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  17. If (tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8, then find xdot

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  18. Prove that t a n^(-1)((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)

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  19. Express sin^(-1)((sin x+ cos x)/(2)), where -(pi)/(4) lt x lt (pi)/(4)...

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  20. Prove that : tan^(-1)x +tan^(-1). (2x)/(1-x^(2)) = tan^(-1) . (3x-x^(...

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